hypothesis space in machine learning python

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Hypothesis in Machine Learning

The concept of a hypothesis is fundamental in Machine Learning and data science endeavors. In the realm of machine learning, a hypothesis serves as an initial assumption made by data scientists and ML professionals when attempting to address a problem. Machine learning involves conducting experiments based on past experiences, and these hypotheses are crucial in formulating potential solutions.

It’s important to note that in machine learning discussions, the terms “hypothesis” and “model” are sometimes used interchangeably. However, a hypothesis represents an assumption, while a model is a mathematical representation employed to test that hypothesis. This section on “Hypothesis in Machine Learning” explores key aspects related to hypotheses in machine learning and their significance.

A hypothesis in machine learning is the model’s presumption regarding the connection between the input features and the result. It is an illustration of the mapping function that the algorithm is attempting to discover using the training set. To minimize the discrepancy between the expected and actual outputs, the learning process involves modifying the weights that parameterize the hypothesis. The objective is to optimize the model’s parameters to achieve the best predictive performance on new, unseen data, and a cost function is used to assess the hypothesis’ accuracy.

What is Hypothesis Testing?

Researchers must consider the possibility that their findings could have happened accidentally before interpreting them. The systematic process of determining whether the findings of a study validate a specific theory that pertains to a population is known as hypothesis testing.

To assess a hypothesis about a population, hypothesis testing is done using sample data. A hypothesis test evaluates the degree of unusualness of the result, determines whether it is a reasonable chance variation, or determines whether the result is too extreme to be attributed to chance.

How does a Hypothesis work?

In most supervised machine learning algorithms, our main goal is to find a possible hypothesis from the hypothesis space that could map out the inputs to the proper outputs. The following figure shows the common method to find out the possible hypothesis from the Hypothesis space:

Hypothesis Space (H)

Hypothesis space is the set of all the possible legal hypothesis. This is the set from which the machine learning algorithm would determine the best possible (only one) which would best describe the target function or the outputs.

Hypothesis (h)

A hypothesis is a function that best describes the target in supervised machine learning. The hypothesis that an algorithm would come up depends upon the data and also depends upon the restrictions and bias that we have imposed on the data.

The Hypothesis can be calculated as:

• m = slope of the lines
• b = intercept

To better understand the Hypothesis Space and Hypothesis consider the following coordinate that shows the distribution of some data:

Say suppose we have test data for which we have to determine the outputs or results. The test data is as shown below:

We can predict the outcomes by dividing the coordinate as shown below:

So the test data would yield the following result:

But note here that we could have divided the coordinate plane as:

The way in which the coordinate would be divided depends on the data, algorithm and constraints.

• All these legal possible ways in which we can divide the coordinate plane to predict the outcome of the test data composes of the Hypothesis Space.
• Each individual possible way is known as the hypothesis.

Hence, in this example the hypothesis space would be like:

Hypothesis in Statistics

In statistics , a hypothesis refers to a statement or assumption about a population parameter. It is a proposition or educated guess that helps guide statistical analyses. There are two types of hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1 or Ha).

• Null Hypothesis(H 0 ): This hypothesis suggests that there is no significant difference or effect, and any observed results are due to chance. It often represents the status quo or a baseline assumption.
• Aternative Hypothesis(H 1 or H a ): This hypothesis contradicts the null hypothesis, proposing that there is a significant difference or effect in the population. It is what researchers aim to support with evidence.

Frequently Asked Questions (FAQs)

1. how does the training process use the hypothesis.

The learning algorithm uses the hypothesis as a guide to minimise the discrepancy between expected and actual outputs by adjusting its parameters during training.

2. How is the hypothesis’s accuracy assessed?

Usually, a cost function that calculates the difference between expected and actual values is used to assess accuracy. Optimising the model to reduce this expense is the aim.

3. What is Hypothesis testing?

Hypothesis testing is a statistical method for determining whether or not a hypothesis is correct. The hypothesis can be about two variables in a dataset, about an association between two groups, or about a situation.

4. What distinguishes the null hypothesis from the alternative hypothesis in machine learning experiments?

The null hypothesis (H0) assumes no significant effect, while the alternative hypothesis (H1 or Ha) contradicts H0, suggesting a meaningful impact. Statistical testing is employed to decide between these hypotheses.

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Best Guesses: Understanding The Hypothesis in Machine Learning

• February 22, 2024
• General , Supervised Learning , Unsupervised Learning

Machine learning is a vast and complex field that has inherited many terms from other places all over the mathematical domain.

It can sometimes be challenging to get your head around all the different terminologies, never mind trying to understand how everything comes together.

In this blog post, we will focus on one particular concept: the hypothesis.

While you may think this is simple, there is a little caveat regarding machine learning.

The statistics side and the learning side.

Don’t worry; we’ll do a full breakdown below.

You’ll learn the following:

What Is a Hypothesis in Machine Learning?

• Is This any different than the hypothesis in statistics?
• What is the difference between the alternative hypothesis and the null?
• Why do we restrict hypothesis space in artificial intelligence?
• Example code performing hypothesis testing in machine learning

In machine learning, the term ‘hypothesis’ can refer to two things.

First, it can refer to the hypothesis space, the set of all possible training examples that could be used to predict or answer a new instance.

Second, it can refer to the traditional null and alternative hypotheses from statistics.

Since machine learning works so closely with statistics, 90% of the time, when someone is referencing the hypothesis, they’re referencing hypothesis tests from statistics.

Is This Any Different Than The Hypothesis In Statistics?

In statistics, the hypothesis is an assumption made about a population parameter.

The statistician’s goal is to prove it true or disprove it.

This will take the form of two different hypotheses, one called the null, and one called the alternative.

Usually, you’ll establish your null hypothesis as an assumption that it equals some value.

For example, in Welch’s T-Test Of Unequal Variance, our null hypothesis is that the two means we are testing (population parameter) are equal.

This means our null hypothesis is that the two population means are the same.

We run our statistical tests, and if our p-value is significant (very low), we reject the null hypothesis.

This would mean that their population means are unequal for the two samples you are testing.

Usually, statisticians will use the significance level of .05 (a 5% risk of being wrong) when deciding what to use as the p-value cut-off.

What Is The Difference Between The Alternative Hypothesis And The Null?

The null hypothesis is our default assumption, which we are trying to prove correct.

The alternate hypothesis is usually the opposite of our null and is much broader in scope.

For most statistical tests, the null and alternative hypotheses are already defined.

You are then just trying to find “significant” evidence we can use to reject our null hypothesis.

These two hypotheses are easy to spot by their specific notation. The null hypothesis is usually denoted by H₀, while H₁ denotes the alternative hypothesis.

Example Code Performing Hypothesis Testing In Machine Learning

Since there are many different hypothesis tests in machine learning and data science, we will focus on one of my favorites.

This test is Welch’s T-Test Of Unequal Variance, where we are trying to determine if the population means of these two samples are different.

There are a couple of assumptions for this test, but we will ignore those for now and show the code.

You can read more about this here in our other post, Welch’s T-Test of Unequal Variance .

We see that our p-value is very low, and we reject the null hypothesis.

What Is The Difference Between The Biased And Unbiased Hypothesis Spaces?

The difference between the Biased and Unbiased hypothesis space is the number of possible training examples your algorithm has to predict.

The unbiased space has all of them, and the biased space only has the training examples you’ve supplied.

Since neither of these is optimal (one is too small, one is much too big), your algorithm creates generalized rules (inductive learning) to be able to handle examples it hasn’t seen before.

Here’s an example of each:

Example of The Biased Hypothesis Space In Machine Learning

The Biased Hypothesis space in machine learning is a biased subspace where your algorithm does not consider all training examples to make predictions.

This is easiest to see with an example.

Let’s say you have the following data:

Happy  and  Sunny  and  Stomach Full  = True

Whenever your algorithm sees those three together in the biased hypothesis space, it’ll automatically default to true.

This means when your algorithm sees:

Sad  and  Sunny  And  Stomach Full  = False

It’ll automatically default to False since it didn’t appear in our subspace.

This is a greedy approach, but it has some practical applications.

Example of the Unbiased Hypothesis Space In Machine Learning

The unbiased hypothesis space is a space where all combinations are stored.

We can use re-use our example above:

This would start to breakdown as

Happy  = True

Happy  and  Sunny  = True

Happy  and  Stomach Full  = True

Let’s say you have four options for each of the three choices.

This would mean our subspace would need 2^12 instances (4096) just for our little three-word problem.

This is practically impossible; the space would become huge.

So while it would be highly accurate, this has no scalability.

More reading on this idea can be found in our post, Inductive Bias In Machine Learning .

Why Do We Restrict Hypothesis Space In Artificial Intelligence?

We have to restrict the hypothesis space in machine learning. Without any restrictions, our domain becomes much too large, and we lose any form of scalability.

This is why our algorithm creates rules to handle examples that are seen in production. 

This gives our algorithms a generalized approach that will be able to handle all new examples that are in the same format.

Other Quick Machine Learning Tutorials

At EML, we have a ton of cool data science tutorials that break things down so anyone can understand them.

Below we’ve listed a few that are similar to this guide:

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Statistics > Machine Learning

Title: hypothesis spaces for deep learning.

Abstract: This paper introduces a hypothesis space for deep learning that employs deep neural networks (DNNs). By treating a DNN as a function of two variables, the physical variable and parameter variable, we consider the primitive set of the DNNs for the parameter variable located in a set of the weight matrices and biases determined by a prescribed depth and widths of the DNNs. We then complete the linear span of the primitive DNN set in a weak* topology to construct a Banach space of functions of the physical variable. We prove that the Banach space so constructed is a reproducing kernel Banach space (RKBS) and construct its reproducing kernel. We investigate two learning models, regularized learning and minimum interpolation problem in the resulting RKBS, by establishing representer theorems for solutions of the learning models. The representer theorems unfold that solutions of these learning models can be expressed as linear combination of a finite number of kernel sessions determined by given data and the reproducing kernel.

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Genetic algorithm: Hypothesis space search

As already understood from our illustrative example, it is clear that genetic algorithms employ a randomized beam search method to seek maximally fit hypotheses. In the hypothesis space search method, we can see that the gradient descent search in backpropagation moves smoothly from one hypothesis to another. On the other hand, the genetic algorithm search can move much more abruptly. It replaces the parent hypotheses with an offspring that can be very different from the parent. Due to this reason, genetic algorithm search has lower chances of it falling into the same kind of local minima that plaques the gradient descent methods.

There is one practical difficulty that is often encountered in genetic algorithms, it is crowding. Crowding can be defined as the phenomenon in which some individuals that are more fit in comparison to others, reproduce quickly, therefore the copies of this individual take over a larger fraction of the population. Most of the strategies used in the genetic algorithms are inspired by biological evolution. One such other strategy used is fitness sharing, in which the measured fitness of an individual is decreased by the presence of another individual of a similar kind. The third method is to restrict all the individuals to combine to form offspring. To better understand we can say that by allowing individuals of the same kind to recombine, clusters of similar individuals are formed, forming multiple subspecies in the population.

Another method would be to spatially distribute individuals and allow only nearby individuals to combine.

Population evolution and schema theorem.

The schema theorem of Holland is used to mathematically characterize the evolution over time of the population with respect to time. It is based on the concept of schema. So, what is schema? Schema is any string composed of 0s, and 1s, and *s, where * represents null, so a schema 0*10, is the same as 0010 and 0110. The schema theorem characterizes the evolution within a genetic algorithm on the basis of the number of instances representing each schema. Let us assume the m(s, t) to denote the number of instances of schema denoted by ‘s’, in the population at the time ‘t’, the expected value in the schema theorem is described as m(s, t+1), in terms of m(s, t), and the other parameters of the population, schema, and GA.

In a genetic algorithm, the evolution of the population depends on the selection step, the recombination step, and the mutation step. The schema theorem is one of the most widely used theorems in the characterization of population evolution within a genetic algorithm. If it fails to consider the positive effects of crossover and mutation, it is in a way incomplete. There are many other recent theoretical analyses that have been proposed, many of these analogies are based on models such as Markov chain models and the statistical mechanical model.

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Artificial Intelligence

In Machine Learning , concept learning can be termed as “ a problem of searching through a predefined space of potential hypothesis for the hypothesis that best fits the training examples” – Tom Mitchell. In this article, we will go through one such concept learning algorithm known as the Find-S algorithm. If you want to go beyond this article and really want the level of expertise in you – you can get certified in Machine Learning Certification!

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The following topics are discussed in this article.

What is Find-S Algorithm in Machine Learning?

• How Does it Work?

Limitations of Find-S Algorithm

Implementation of find-s algorithm.

In order to understand Find-S algorithm, you need to have a basic idea of the following concepts as well:

• Concept Learning
• General Hypothesis
• Specific Hypothesis

1. Concept Learning 

Let’s try to understand concept learning with a real-life example. Most of human learning is based on past instances or experiences. For example, we are able to identify any type of vehicle based on a certain set of features like make, model, etc., that are defined over a large set of features.

These special features differentiate the set of cars, trucks, etc from the larger set of vehicles. These features that define the set of cars, trucks, etc are known as concepts.

Similar to this, machines can also learn from concepts to identify whether an object belongs to a specific category or not. Any algorithm that supports concept learning requires the following:

• Training Data
• Target Concept
• Actual Data Objects

2. General Hypothesis

Hypothesis, in general, is an explanation for something. The general hypothesis basically states the general relationship between the major variables. For example, a general hypothesis for ordering food would be  I want a burger.

G = { ‘?’, ‘?’, ‘?’, …..’?’}

3. Specific Hypothesis

The specific hypothesis fills in all the important details about the variables given in the general hypothesis. The more specific details into the example given above would be  I want a cheeseburger with a chicken pepperoni filling with a lot of lettuce. 

S = {‘Φ’,’Φ’,’Φ’, ……,’Φ’}

Now ,let’s talk about the Find-S Algorithm in Machine Learning.

The Find-S algorithm follows the steps written below:

• Initialize ‘h’ to the most specific hypothesis.
• The Find-S algorithm only considers the positive examples and eliminates negative examples. For each positive example, the algorithm checks for each attribute in the example. If the attribute value is the same as the hypothesis value, the algorithm moves on without any changes. But if the attribute value is different than the hypothesis value, the algorithm changes it to ‘?’.

Now that we are done with the basic explanation of the Find-S algorithm, let us take a look at how it works.

How Does It Work?

• The process starts with initializing ‘h’ with the most specific hypothesis, generally, it is the first positive example in the data set.
• We check for each positive example. If the example is negative, we will move on to the next example but if it is a positive example we will consider it for the next step.
• We will check if each attribute in the example is equal to the hypothesis value.
• If the value matches, then no changes are made.
• If the value does not match, the value is changed to ‘?’.
• We do this until we reach the last positive example in the data set.

There are a few limitations of the Find-S algorithm listed down below:

• There is no way to determine if the hypothesis is consistent throughout the data.
• Inconsistent training sets can actually mislead the Find-S algorithm, since it ignores the negative examples.
• Find-S algorithm does not provide a backtracking technique to determine the best possible changes that could be done to improve the resulting hypothesis.

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Now that we are aware of the limitations of the Find-S algorithm, let us take a look at a practical implementation of the Find-S Algorithm.

To understand the implementation, let us try to implement it to a smaller data set with a bunch of examples to decide if a person wants to go for a walk.

The concept of this particular problem will be on what days does a person likes to go on walk.

Looking at the data set, we have six attributes and a final attribute that defines the positive or negative example. In this case, yes is a positive example, which means the person will go for a walk.

So now, the general hypothesis is:

h 0 = {‘Morning’, ‘Sunny’, ‘Warm’, ‘Yes’, ‘Mild’, ‘Strong’}

This is our general hypothesis, and now we will consider each example one by one, but only the positive examples.

h 1 = {‘Morning’, ‘Sunny’, ‘?’, ‘Yes’, ‘?’, ‘?’}

h 2 = {‘?’, ‘Sunny’, ‘?’, ‘Yes’, ‘?’, ‘?’}

We replaced all the different values in the general hypothesis to get a resultant hypothesis. Now that we know how the Find-S algorithm works, let us take a look at an implementation using Python .

Let’s try to implement the above example using Python . The code to implement the Find-S algorithm using the above data is given below.

This brings us to the end of this article where we have learned the Find-S Algorithm in Mach ine Learning with its implementation and use case. I hope you are clear with all that has been shared with you in this tutorial.

You can also take a  Machine Learning Course  Masters Program. The program will provide you with the most in-depth and practical information on machine-learning applications in real-world situations. Additionally, you’ll learn the essentials needed to be successful in the field of machine learning, such as statistical analysis, Python, and data science.

We are here to help you with every step on your journey and come up with a curriculum that is designed for students and professionals who want to be a   Machine Learning Engineer . The course is designed to give you a head start into Python programming and train you for both core and advanced Python concepts along with various   Machine learning Algorithms   like  SVM ,  Decision Tree , etc.

If you come across any questions, feel free to ask all your questions in the comments section of “Find-S Algorithm In Machine Learning” and our team will be glad to answer.

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